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      SUBROUTINE <a name="CGBCON.1"></a><a href="cgbcon.f.html#CGBCON.1">CGBCON</a>( NORM, N, KL, KU, AB, LDAB, IPIV, ANORM, RCOND,
     $                   WORK, RWORK, INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  -- LAPACK routine (version 3.1) --
</span><span class="comment">*</span><span class="comment">     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment">     November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Modified to call <a name="CLACN2.8"></a><a href="clacn2.f.html#CLACN2.1">CLACN2</a> in place of <a name="CLACON.8"></a><a href="clacon.f.html#CLACON.1">CLACON</a>, 10 Feb 03, SJH.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Scalar Arguments ..
</span>      CHARACTER          NORM
      INTEGER            INFO, KL, KU, LDAB, N
      REAL               ANORM, RCOND
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      INTEGER            IPIV( * )
      REAL               RWORK( * )
      COMPLEX            AB( LDAB, * ), WORK( * )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Purpose
</span><span class="comment">*</span><span class="comment">  =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  <a name="CGBCON.24"></a><a href="cgbcon.f.html#CGBCON.1">CGBCON</a> estimates the reciprocal of the condition number of a complex
</span><span class="comment">*</span><span class="comment">  general band matrix A, in either the 1-norm or the infinity-norm,
</span><span class="comment">*</span><span class="comment">  using the LU factorization computed by <a name="CGBTRF.26"></a><a href="cgbtrf.f.html#CGBTRF.1">CGBTRF</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  An estimate is obtained for norm(inv(A)), and the reciprocal of the
</span><span class="comment">*</span><span class="comment">  condition number is computed as
</span><span class="comment">*</span><span class="comment">     RCOND = 1 / ( norm(A) * norm(inv(A)) ).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Arguments
</span><span class="comment">*</span><span class="comment">  =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  NORM    (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment">          Specifies whether the 1-norm condition number or the
</span><span class="comment">*</span><span class="comment">          infinity-norm condition number is required:
</span><span class="comment">*</span><span class="comment">          = '1' or 'O':  1-norm;
</span><span class="comment">*</span><span class="comment">          = 'I':         Infinity-norm.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  N       (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The order of the matrix A.  N &gt;= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  KL      (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The number of subdiagonals within the band of A.  KL &gt;= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  KU      (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The number of superdiagonals within the band of A.  KU &gt;= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  AB      (input) COMPLEX array, dimension (LDAB,N)
</span><span class="comment">*</span><span class="comment">          Details of the LU factorization of the band matrix A, as
</span><span class="comment">*</span><span class="comment">          computed by <a name="CGBTRF.52"></a><a href="cgbtrf.f.html#CGBTRF.1">CGBTRF</a>.  U is stored as an upper triangular band
</span><span class="comment">*</span><span class="comment">          matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and
</span><span class="comment">*</span><span class="comment">          the multipliers used during the factorization are stored in
</span><span class="comment">*</span><span class="comment">          rows KL+KU+2 to 2*KL+KU+1.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDAB    (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the array AB.  LDAB &gt;= 2*KL+KU+1.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  IPIV    (input) INTEGER array, dimension (N)
</span><span class="comment">*</span><span class="comment">          The pivot indices; for 1 &lt;= i &lt;= N, row i of the matrix was
</span><span class="comment">*</span><span class="comment">          interchanged with row IPIV(i).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  ANORM   (input) REAL
</span><span class="comment">*</span><span class="comment">          If NORM = '1' or 'O', the 1-norm of the original matrix A.
</span><span class="comment">*</span><span class="comment">          If NORM = 'I', the infinity-norm of the original matrix A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  RCOND   (output) REAL
</span><span class="comment">*</span><span class="comment">          The reciprocal of the condition number of the matrix A,
</span><span class="comment">*</span><span class="comment">          computed as RCOND = 1/(norm(A) * norm(inv(A))).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  WORK    (workspace) COMPLEX array, dimension (2*N)
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  RWORK   (workspace) REAL array, dimension (N)
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  INFO    (output) INTEGER
</span><span class="comment">*</span><span class="comment">          = 0:  successful exit
</span><span class="comment">*</span><span class="comment">          &lt; 0: if INFO = -i, the i-th argument had an illegal value
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Parameters ..
</span>      REAL               ONE, ZERO
      PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      LOGICAL            LNOTI, ONENRM
      CHARACTER          NORMIN
      INTEGER            IX, J, JP, KASE, KASE1, KD, LM
      REAL               AINVNM, SCALE, SMLNUM
      COMPLEX            T, ZDUM
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Arrays ..
</span>      INTEGER            ISAVE( 3 )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Functions ..
</span>      LOGICAL            <a name="LSAME.97"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
      INTEGER            ICAMAX
      REAL               <a name="SLAMCH.99"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>
      COMPLEX            CDOTC
      EXTERNAL           <a name="LSAME.101"></a><a href="lsame.f.html#LSAME.1">LSAME</a>, ICAMAX, <a name="SLAMCH.101"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>, CDOTC
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Subroutines ..
</span>      EXTERNAL           CAXPY, <a name="CLACN2.104"></a><a href="clacn2.f.html#CLACN2.1">CLACN2</a>, <a name="CLATBS.104"></a><a href="clatbs.f.html#CLATBS.1">CLATBS</a>, <a name="CSRSCL.104"></a><a href="csrscl.f.html#CSRSCL.1">CSRSCL</a>, <a name="XERBLA.104"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Intrinsic Functions ..
</span>      INTRINSIC          ABS, AIMAG, MIN, REAL
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Statement Functions ..
</span>      REAL               CABS1
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Statement Function definitions ..
</span>      CABS1( ZDUM ) = ABS( REAL( ZDUM ) ) + ABS( AIMAG( ZDUM ) )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Test the input parameters.
</span><span class="comment">*</span><span class="comment">
</span>      INFO = 0
      ONENRM = NORM.EQ.<span class="string">'1'</span> .OR. <a name="LSAME.120"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( NORM, <span class="string">'O'</span> )
      IF( .NOT.ONENRM .AND. .NOT.<a name="LSAME.121"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( NORM, <span class="string">'I'</span> ) ) THEN
         INFO = -1
      ELSE IF( N.LT.0 ) THEN
         INFO = -2
      ELSE IF( KL.LT.0 ) THEN
         INFO = -3
      ELSE IF( KU.LT.0 ) THEN
         INFO = -4
      ELSE IF( LDAB.LT.2*KL+KU+1 ) THEN
         INFO = -6
      ELSE IF( ANORM.LT.ZERO ) THEN
         INFO = -8
      END IF
      IF( INFO.NE.0 ) THEN
         CALL <a name="XERBLA.135"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="CGBCON.135"></a><a href="cgbcon.f.html#CGBCON.1">CGBCON</a>'</span>, -INFO )
         RETURN
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Quick return if possible
</span><span class="comment">*</span><span class="comment">
</span>      RCOND = ZERO
      IF( N.EQ.0 ) THEN
         RCOND = ONE
         RETURN
      ELSE IF( ANORM.EQ.ZERO ) THEN
         RETURN
      END IF
<span class="comment">*</span><span class="comment">
</span>      SMLNUM = <a name="SLAMCH.149"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>( <span class="string">'Safe minimum'</span> )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Estimate the norm of inv(A).
</span><span class="comment">*</span><span class="comment">
</span>      AINVNM = ZERO
      NORMIN = <span class="string">'N'</span>
      IF( ONENRM ) THEN
         KASE1 = 1
      ELSE
         KASE1 = 2
      END IF
      KD = KL + KU + 1
      LNOTI = KL.GT.0
      KASE = 0
   10 CONTINUE
      CALL <a name="CLACN2.164"></a><a href="clacn2.f.html#CLACN2.1">CLACN2</a>( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
      IF( KASE.NE.0 ) THEN
         IF( KASE.EQ.KASE1 ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Multiply by inv(L).
</span><span class="comment">*</span><span class="comment">
</span>            IF( LNOTI ) THEN
               DO 20 J = 1, N - 1
                  LM = MIN( KL, N-J )
                  JP = IPIV( J )
                  T = WORK( JP )
                  IF( JP.NE.J ) THEN
                     WORK( JP ) = WORK( J )
                     WORK( J ) = T
                  END IF
                  CALL CAXPY( LM, -T, AB( KD+1, J ), 1, WORK( J+1 ), 1 )
   20          CONTINUE
            END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Multiply by inv(U).
</span><span class="comment">*</span><span class="comment">
</span>            CALL <a name="CLATBS.185"></a><a href="clatbs.f.html#CLATBS.1">CLATBS</a>( <span class="string">'Upper'</span>, <span class="string">'No transpose'</span>, <span class="string">'Non-unit'</span>, NORMIN, N,
     $                   KL+KU, AB, LDAB, WORK, SCALE, RWORK, INFO )
         ELSE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Multiply by inv(U').
</span><span class="comment">*</span><span class="comment">
</span>            CALL <a name="CLATBS.191"></a><a href="clatbs.f.html#CLATBS.1">CLATBS</a>( <span class="string">'Upper'</span>, <span class="string">'Conjugate transpose'</span>, <span class="string">'Non-unit'</span>,
     $                   NORMIN, N, KL+KU, AB, LDAB, WORK, SCALE, RWORK,
     $                   INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Multiply by inv(L').
</span><span class="comment">*</span><span class="comment">
</span>            IF( LNOTI ) THEN
               DO 30 J = N - 1, 1, -1
                  LM = MIN( KL, N-J )
                  WORK( J ) = WORK( J ) - CDOTC( LM, AB( KD+1, J ), 1,
     $                        WORK( J+1 ), 1 )
                  JP = IPIV( J )
                  IF( JP.NE.J ) THEN
                     T = WORK( JP )
                     WORK( JP ) = WORK( J )
                     WORK( J ) = T
                  END IF
   30          CONTINUE
            END IF
         END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Divide X by 1/SCALE if doing so will not cause overflow.
</span><span class="comment">*</span><span class="comment">
</span>         NORMIN = <span class="string">'Y'</span>
         IF( SCALE.NE.ONE ) THEN
            IX = ICAMAX( N, WORK, 1 )
            IF( SCALE.LT.CABS1( WORK( IX ) )*SMLNUM .OR. SCALE.EQ.ZERO )
     $         GO TO 40
            CALL <a name="CSRSCL.219"></a><a href="csrscl.f.html#CSRSCL.1">CSRSCL</a>( N, SCALE, WORK, 1 )
         END IF
         GO TO 10
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Compute the estimate of the reciprocal condition number.
</span><span class="comment">*</span><span class="comment">
</span>      IF( AINVNM.NE.ZERO )
     $   RCOND = ( ONE / AINVNM ) / ANORM
<span class="comment">*</span><span class="comment">
</span>   40 CONTINUE
      RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     End of <a name="CGBCON.232"></a><a href="cgbcon.f.html#CGBCON.1">CGBCON</a>
</span><span class="comment">*</span><span class="comment">
</span>      END

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